Class 10 ICSE Maths Solution – Complete Guide with Answers

Class 10 ICSE Maths Solution provides all questions and answers for better understanding and practice. Perfect resource for exam preparation.

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Maths can be challenging for students, but with the right practice and understanding of key concepts, it can become much more manageable. This article covers the essential solutions for Class 10 ICSE Maths, offering detailed answers to the most frequently asked questions. Whether you're preparing for exams or simply seeking to improve your knowledge, this guide aims to provide clear, straightforward solutions. These solutions will cover a variety of topics, from algebra to geometry, and beyond. With over 50 questions and their answers, this resource is designed to help students in their preparation.

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Topic: Class 10 ICSE Maths Solutions

Topic	Concepts Covered	Types of Questions
Algebra	Quadratic equations, Polynomials	Solve for x, Factorization, Roots of equations
Geometry	Circles, Trigonometry, Constructions	Prove theorems, Solve for angles
Mensuration	Surface Area, Volume, Areas of shapes	Solve for area, Volume, Surface area
Probability	Basic Probability	Find the probability of events
Statistics	Mean, Median, Mode	Calculate measures of central tendency

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Question 1
Question: What is the sum of the angles in a triangle?
Answer: The sum of the angles in a triangle is always 180°.

Question 2
Question: What is the formula for the area of a circle?
Answer: The formula for the area of a circle is A = πr², where r is the radius.

Question 3
Question: What is a quadratic equation?
Answer: A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants.

Question 4
Question: What is the Pythagorean Theorem?
Answer: The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it is written as a² + b² = c².

Question 5
Question: What is the formula for the volume of a cylinder?
Answer: The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.

Question 6
Question: How do you calculate the mean of a set of numbers?
Answer: To calculate the mean, add all the numbers together and divide the sum by the total number of values.

Question 7
Question: What is the relationship between a line and a plane?
Answer: A line can either intersect a plane at a single point or be parallel to it, or even lie in the plane.

Question 8
Question: What is the formula for the surface area of a sphere?
Answer: The formula for the surface area of a sphere is A = 4πr², where r is the radius.

Question 9
Question: What are the different types of angles?
Answer: The different types of angles are acute, obtuse, right, straight, and reflex angles.

Question 10
Question: What is a polynomial?
Answer: A polynomial is an expression consisting of variables raised to powers and coefficients. An example is 3x² + 5x + 2.

Question 11
Question: How do you solve a pair of linear equations?
Answer: A pair of linear equations can be solved using methods like substitution, elimination, or matrix method.

Question 12
Question: What is the distance formula?
Answer: The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²), used to calculate the distance between two points in a plane.

Question 13
Question: What is the formula for the area of a triangle?
Answer: The area of a triangle is given by A = ½bh, where b is the base and h is the height.

Question 14
Question: What is the difference between permutation and combination?
Answer: Permutation refers to the arrangement of items, while combination refers to the selection of items without regard to order.

Question 15
Question: What is the formula for the surface area of a cone?
Answer: The surface area of a cone is given by A = πr(r + l), where r is the radius and l is the slant height.

Question 16
Question: What is a probability?
Answer: Probability is the measure of the likelihood of an event happening, and it is calculated as the number of favorable outcomes divided by the total number of outcomes.

Question 17
Question: What are co-interior angles?
Answer: Co-interior angles are the pair of angles on the same side of the transversal and inside the two lines, and their sum is 180°.

Question 18
Question: What is the formula for the area of a rectangle?
Answer: The area of a rectangle is given by A = l × w, where l is the length and w is the width.

Question 19
Question: How do you calculate the mode of a set of numbers?
Answer: The mode is the value that appears most frequently in the data set.

Question 20
Question: What is the relationship between the chords and the circle?
Answer: A chord is a line segment joining two points on a circle, and the longest chord is the diameter.

Question 21
Question: What is the formula for the area of a trapezium?
Answer: The area of a trapezium is given by A = ½(a + b)h, where a and b are the lengths of the parallel sides and h is the height.

Question 22
Question: What is an arithmetic progression?
Answer: An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.

Question 23
Question: How do you find the median of a set of numbers?
Answer: The median is the middle value when the numbers are arranged in ascending or descending order. If there is an even number of terms, it is the average of the two middle terms.

Question 24
Question: What is the law of sines in trigonometry?
Answer: The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

Question 25
Question: What is the formula for the area of a rhombus?
Answer: The area of a rhombus is given by A = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

Question 26
Question: How do you calculate the volume of a cone?
Answer: The volume of a cone is calculated using the formula V = ⅓πr²h, where r is the radius and h is the height.

Question 27
Question: What is the difference between scalar and vector quantities?
Answer: Scalar quantities have only magnitude, while vector quantities have both magnitude and direction.

Question 28
Question: What is the formula for the volume of a sphere?
Answer: The volume of a sphere is given by V = ⁴/₃πr³, where r is the radius.

Question 29
Question: What is the formula for the perimeter of a rectangle?
Answer: The perimeter of a rectangle is given by P = 2(l + w), where l is the length and w is the width.

Question 30
Question: What is the difference between acute and obtuse angles?
Answer: Acute angles are less than 90°, while obtuse angles are greater than 90° but less than 180°.

Question 31
Question: How do you find the roots of a quadratic equation?
Answer: The roots of a quadratic equation can be found using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a.

Question 32
Question: What is the formula for the area of a parallelogram?
Answer: The area of a parallelogram is given by A = bh, where b is the base and h is the height.

Question 33
Question: How do you calculate the mean deviation?
Answer: The mean deviation is the average of the absolute differences between each data point and the mean.

Question 34
Question: What is the law of cosines?
Answer: The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is written as c² = a² + b² - 2ab cos C.

Question 35
Question: What is a factor in algebra?
Answer: A factor is a number or expression that divides another number or expression without leaving a remainder.

Question 36
Question: What is the formula for the surface area of a cube?
Answer: The surface area of a cube is given by A = 6a², where a is the length of an edge.

Question 37
Question: How do you find the probability of multiple events?
Answer: The probability of multiple independent events is the product of their individual probabilities.

Question 38
Question: What is the formula for the perimeter of a circle?
Answer: The perimeter of a circle, also known as the circumference, is given by C = 2πr, where r is the radius.

Question 39
Question: What is the concept of a tangent to a circle?
Answer: A tangent is a straight line that touches a circle at exactly one point.

Question 40
Question: How do you solve problems involving time and work?
Answer: Time and work problems can be solved by using the formula: Work = Rate × Time, and the combined work of multiple workers is the sum of their individual rates.

Question 41
Question: What is the formula for the surface area of a hemisphere?
Answer: The surface area of a hemisphere is A = 3πr², where r is the radius.

Question 42
Question: What is the equation of a straight line in slope-intercept form?
Answer: The equation of a straight line is given by y = mx + b, where m is the slope and b is the y-intercept.

Question 43
Question: What is the formula for the area of a sector of a circle?
Answer: The area of a sector is given by A = (θ/360) × πr², where θ is the angle in degrees and r is the radius.

Question 44
Question: What is the relationship between the radius and diameter of a circle?
Answer: The diameter is twice the radius, i.e., d = 2r.

Question 45
Question: What is a reflection in geometry?
Answer: A reflection is a transformation where each point of an object is mirrored across a line, called the line of reflection.

Question 46
Question: How do you find the probability of drawing a red card from a deck of cards?
Answer: The probability is calculated by dividing the number of red cards (26) by the total number of cards (52), so the probability is 26/52 = ½.

Question 47
Question: What is the difference between sine and cosine functions?
Answer: The sine function gives the ratio of the opposite side to the hypotenuse, while the cosine function gives the ratio of the adjacent side to the hypotenuse in a right triangle.

Question 48
Question: What is the formula for the volume of a pyramid?
Answer: The volume of a pyramid is given by V = ⅓ × base area × height.

Question 49
Question: What is an isosceles triangle?
Answer: An isosceles triangle is a triangle that has two sides of equal length.

Question 50
Question: What is the formula for the area of a circle?
Answer: The area of a circle is A = πr², where r is the radius.

Question 51
Question: How do you find the sum of an arithmetic progression?
Answer: The sum of an arithmetic progression is given by S = n/2 × (2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference.

Question 52
Question: What is the sum of the interior angles of a polygon?
Answer: The sum of the interior angles of a polygon is given by (n-2) × 180°, where n is the number of sides.

Question 53
Question: What is the difference between a function and a relation?
Answer: A function is a special type of relation where every input has exactly one output.

Question 54
Question: What is a circle's radius?
Answer: The radius of a circle is the distance from the center to any point on the circle.

Question 55
Question: How do you find the length of the hypotenuse in a right-angled triangle?
Answer: The length of the hypotenuse can be found using the Pythagorean theorem: c = √(a² + b²).

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